Question

When the price of a commodity is $.10, an individual buys 40 units of it. When the price falls to $.8 what would be elasticity of demand, if demand increase to (i)44 units, (ii) 50 units ?

Answer 1

$\bf Answers$

$(a) \space \eta_{p} = -0.4$ $\space (Inelastic)$

$(b) \space \eta_{p} = -1$ $\space (Unitary)$

$\bf Solutions$

We are given:

$P_{0} = \$10, \\ Q_{0} = 40 \space units, \space and \\ P_{1} = \$8$

$PED (\eta_{p}) = \dfrac {\% \space ∆ \space in \space Quantity \space demanded} {\% \space ∆ \space in \space price}$

$\% \space ∆ \space in \space price = \dfrac {(8-10)}{8} × 100\%$

$= \dfrac {-2}{8} × 100\%$

$= -25\%$

$(a) \space Q_{1} = 44 \space units \\$

$\% \space ∆ \space in \space quantity \space demanded$

$= \dfrac {(44 - 40)}{40} × 100\%$

$= \dfrac {4}{40}×100\%$

$= +10\%$

$\eta_{p} = -\dfrac {10\%}{25\%}$

$=\bf -0.4 \space (Inelastic)$

$(b) \space Q_{1} = 50 \space units$

$\% \space ∆ \space in \space quantity \space demanded$

$= \dfrac {(50-40)}{40}×100\%$

$= \dfrac {10}{40}×100\%$

$= +25\%$

$\eta_{p} = -\dfrac {25\%}{25\%}$

$= \bf -1 (Unitary)$